Umi no Yami, Tsuki no Kage

Umi no Yami, Tsuki no Kage (海の闇、月の影, translated as Darkness of the Sea, Shadow of the Moon), is an 18-volumes shoujo manga by Chie Shinohara, the author of Anatolia Story. It ran in Shogakukan's Shoujo Comic magazine in the late 80's, and it had a 3-OAV anime adaptation in 1989.

The twin sisters Ruka and Rumi Kobayakawa are highschool students and both crush on their handsome sempai, Katsuyuki Touma. When Katsuyuki asks the younger twin Ruka out and Ruka hesitates because she doesn't want "betray" Rumi's feelings, Rumi does her best to be supportive of her sister, but it looks like deep down seems to feel kinda betrayed by her.

The girls and the other members of their track team go out to the beach, but are trapped in a cave during a storm in the middle of a party. The place turns out to be an old burial ground, then an odd bacteria is released and all the girls in the group are fatally poisoned by it, save for the twins. . .

The Kobayakawas not only survive, but are "given" strange and terrifying Psychic Powers beyond their imagination. But the worst consequence is then horrible shift in the personality of the once sweet and normal Rumi, who almost immediately transforms into a merciless, spiteful and cruel girl who will stop at nothing to get Katsuyuki for herself - even if she has to eliminate her twin to get him. So the still kind-hearted Ruka must learn how to control her own powers and, with the support of Katsuyuki, try to find a way to stop Rumi and turn her back to the kind girl she used to be.

Tropes used in Umi no Yami, Tsuki no Kage include:

• The Ace: Katsuyuki
• Academic Athlete: Katsuyuki is not only a track team star, but also quite booksmart and not bad at Doing Research
• Always Identical Twins: Rumi and Ruka
• Badass Biker: Katsuyuki
• Cain and Abel: Rumi is the Cain, Ruka is the Abel.
• Evil Twin: Rumi, holy shit. It seems to be due to Demonic Possession, though, and Ruka and Katsuyuki hope that they will be able to save her.
• Face-Heel Turn: Rumi. Again, holy shit.
• Falling Into His Arms: Subverted: Katsuyuki tells Ruka to do this when her hospital room (on a high floor) is on fire - but as she jumps off the window and towards him, her Flight powers activate.
• Gory Discretion Shot: When Rumi kills Asako because she bullied her over Katsuyuki, one only sees Rumi pinning the other girl to a tree and then phasing her fingers through Asako's head, but not the actual murder - save for Rumi's face being splattered with blood, plus her Slasher Smile. When Ruka goes see what's going on, she finds Asako's corpse on the ground and all bloody.
• The Glorious War of Sisterly Rivalry: Rumi is an evil version of the Smart Sister, while Ruka becomes the Beautiful Sister.
• How Do I Shot Web?: Ruka, compared to Rumi.
• Japanese School Club: The twins and Katsuyuki are members of their school's track teams.
• Light Feminine and Dark Feminine: Ruka is the Light, Rumi is the Dark.
• Motherly Side Plait: Asako was not a mother, but she styled her hair like this. Guess what happens to her...?
• Murder the Hypotenuse: If Rumi has to do this to get Katsuyuki for herself? She will.
• Nightmare Face: Rumi is ADDICTED to making those, especially in the manga.
• Psychic Powers: The twins obtain these, which include: Flight, intangibility, illusions...
• Sailor Fuku: Averted: the kids' school has Western uniforms.
• Sempai-Kohai: Katsuyuki is older than the girls.
• Sibling Triangle: Between the twins and Katsuyuki. He picked Ruka from the very start, and Rumi initially supported them. . . but the virus that mutated the girls changed everything.
• Shoujo Demographic: The rare kind that throws horror into the mix.
• Sole Survivor: All the other girls who got in the cave died of poisoning, with Ruka and Rumi barely managing to escape this fate.
• Stock Shoujo Bullying Tactics: An older girl named Asako tries to harass Rumi over Katsuyuki, believing her to be Ruka. The poor, poor fool. 
• Understanding Boyfriend: Katsuyuki tries his best to be this to Ruka. 
• Yandere: RUMI!